# Short-Term Electric Load and Price Forecasting Using Enhanced Extreme Learning Machine Optimization in Smart Grids

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## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Problem Statement

#### 1.3. Contributions

- Feature engineering is performed using Recursive Feature Elimination (RFE), Classification And Regression Technique (CART) and Relief-F
- Two new classification techniques are proposed, i.e., Enhanced Logistic Regression (ELR) and Enhanced Recurrent Extreme Learning Machine (ERELM)
- In ELR, the loss function of Logistic Regression (LR) is modified to increase the prediction accuracy
- The Grey Wolf Optimizer (GWO) learning algorithm is used with Recurrent Extreme Learning Machine (RELM) to optimize weights and biases in order to improve the forecasting accuracy
- The proposed techniques predict the electricity load and price efficiently
- ELR is used to predict the load and price of a smart home, whereas ERELM is used for forecasting the load of smart meters
- Cross validation is performed using K-Fold and Monte Carlo methods for assigning the fixed optimal values to weights and biases. This further increases the efficiency of GWO
- The accuracy of the proposed techniques is evaluated using the performance metrics, i.e., Mean Absolute Error (MAE), Mean Square Error (MSE), Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE)

## 2. Related Work

#### 2.1. Electricity Load Forecasting

#### 2.2. Electricity Price Forecasting

## 3. Existing and New Techniques

#### 3.1. Classification and Regression Technique (CART)

- Construction of maximum tree,
- Choice of right tree size,
- Classification of data using the constructed tree.

- Problem definition,
- Variable selection,
- Specifying the accuracy criteria,
- Selecting split size,
- Determine the threshold to stop splitting,
- Selection of the best tree.

#### 3.2. Recursive Feature Elimination (RFE)

Algorithm 1: Pseudocode of RFE |

#### 3.3. Relief-F

Algorithm 2: Pseudocode of Relief-F |

#### 3.4. Convolutional Neural Network (CNN)

#### 3.5. Logistic Regression (LR)

#### 3.6. Enhanced Logistic Regression (ELR)

#### 3.7. Grey Wolf Optimizer (GWO)

- Parameters of grey wolves are initialized such as maximum number of iterations, the population size, upper and lower bounds of search space,
- Calculate fitness value to initialize the position of each wolf,
- Select three best wolves, i.e., $\alpha $, $\beta $ and $\gamma $,
- Calculate the positions of the remaining wolves ($\omega $),
- Repeat from step 2 if current solution is not satisfied,
- The fittest solution is taken as $\alpha $.

Algorithm 3: Pseudocode of GWO |

#### 3.8. Recurrent Extreme Learning Machine (RELM)

#### 3.9. Enhanced Recurrent Extreme Learning Machine (ERELM)

Algorithm 4: Pseudocode of ERELM |

## 4. Proposed System Models

#### 4.1. Proposed System Model 1

#### 4.2. Proposed System Model 2

## 5. Simulation Results and Discussion

#### 5.1. Simulation Results and Discussion of Proposed System Model 1

#### 5.1.1. Data Description

#### 5.1.2. CART

#### 5.1.3. RFE

#### 5.1.4. Relief-F

#### 5.1.5. Load Forecasting

#### 5.1.6. Price Forecasting

#### 5.2. Simulation Results and Discussion of Proposed System Model 2

#### 5.2.1. Data Description

#### 5.2.2. Results Discussion

## 6. Performance Metrics

## 7. Conclusions and Future Work

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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TG | SG |
---|---|

Analogue | Digital |

One way communication | Two way communication |

Centralized power generation | Distributed power generation |

Small number of sensors | Large number of sensors |

Manual monitoring | Automatic monitoring |

Difficult to locate failures | Easy to locate failures |

Abbreviation | Full Form |
---|---|

AEMO | Australia Electricity Market Operators |

AI | Artificially Intelligent |

ANN | Artificial Neural Network |

ARIMA | Auto Regressive Integrated Moving Average |

ARMAX | Auto Regressive Moving Average with Exogenous variables |

BP | Back Propagation |

CART | Classification and Regression Technique |

CNN | Convolutional Neural Network |

DAE | Deep Auto Encoders |

DE-SVM | Differential Evolution Support Vector Machine |

DNN | Deep Neural Network |

DRN | Deep Residual Network |

DSM | Demand Side Management |

DWT | Discrete Wavelet Transform |

ELM | Extreme Learning Machine |

EPEX | European Power Exchange |

ELR | Enhanced Logistic Regression |

ERELM | Enhanced Recurrent Extreme Learning Machine |

FFNN | Feed Forward Neural Network |

GCA | Gray Correlation Analysis |

GWO | Grey Wolf Optimization |

GRU | Gated Recurrent Unit |

ISO NECA | Independent System Operator New England Control Area |

KELM | Kernel Extreme Learning Machine |

KPCA | Kernel Principal Component Analysis |

LR | Logistic Regression |

LSTM | Long Short Term Memory |

MAE | Mean Absolute Error |

MAPE | Mean Absolute Percentage Error |

MISO | Midcontinent Independent System Operator |

MLP | Multi Layer Perceptron |

MLR | Multi Linear Regression |

MSE | Mean Square Error |

NLS-SVM | Nonlinear Least Square Support Vector Machine |

NN | Neural Network |

NYISO | New York Independent System Operator |

OS-ELM7 | Online Sequential Extreme Learning Machine |

PJM | Pennsylvania–New Jersey–Maryland |

PSO | Particle Swarm Optimization |

RBM | Restricted Boltzmann Machine |

RELM | Recurrent Extreme Learning Machne |

ReLU | Rectified Linear Unit |

RES | Renewable Energy Sources |

RFE | Recursive Feature Elimination |

RMSE | Root Mean Square Error |

RNN | Recurrent Neural Network |

SARIMA | Seasonal Auto Regressive Integrated Moving Average |

SBELM | Sparse Bayesian Extreme Learning Machine |

SDA | Stacked De-noising Autoencoders |

SG | Smart Grid |

SLFN | Single Layer Feedforward Network |

SM | Smart Meters |

TG | Traditional Grid |

TVC-ABC | Time Varying Coefficients Artificial Bee Colony |

Symbol | Description |
---|---|

x | Actual value |

x’ | Predicted value |

t | Time slot |

y | Output |

h | Step size |

m | Mean |

${A}_{v}$ | Actual value |

${F}_{v}$ | Forecasted value |

T | Total time duration |

N | Total number of samples |

$\alpha $ | Fittest wolf 1 |

$\beta $ | Fittest wolf 2 |

$\delta $ | Fittest wolf 3 |

$\omega $ | Remaining wolves |

Technique | Features/DataSet | Region | Contributions | Limitations |
---|---|---|---|---|

Bayesian, MLP [8] | Load/UKDale | UK | Forecasting done using behavioural analytic | Requires intensive training |

MLR, BaggedT, NN [9] | Load and weather/Beijing | Beijing, China | Comparison between techniques done to overcome the limitations | Not suitable for long term forecasting |

DRN [10] | Load and weather/ISO-NE | New England | Load forecasting done using weather data | Over fitting |

RBM, ReLU [11] | Load/Korea Electric Company | Korea | Two stage forecasting performed | Long-term forecasting not supported |

DWT-IR, SVM, SWA [12] | Load/NYISO, AEMO | Australia, US | Dimensionality reduction and paramater optimization done | Time complexity |

Modified MI, ANN [13] | Load/PJM | US | Two stage forecasting is done | Time complexity |

DAE [14] | Load/Hong Kong | Hong Kong | Cooling load prediction done | Time and space consuming |

Pooling Deep RNN [15] | Load/IRISH | Ireland | Pooling of consumers done for aggregated prediction | Difficult to train |

ELM [16,17] | Load/USF | US | Long, medium and short term forecasting done | Over fitting |

SLFN [18,19] | Load/Marine Resources Division | Australia | Optimization of weights | Overfitting by using moore-penrose inverse |

Sparse Bayesian ELM [20] | Electricity Load/Harvard medical college | USA | Optimization of weights and biases using BP | Require intensive training |

PSO, DPSO [21] | Load/US | USA | Compact ANNs are produced | Large computational time |

GWO with NN [22] | USA | Weights and biases optimization | Time complexity | |

RELM [6,23] | Electricity Load/Bench mark UCI machine | Portugal | Use of context neurons | Computationally expensive |

LSTM, DNN, GRU [24] | Load and price/EPEX | Belgium | Comparison between different models | Over fitting |

Hilbertian, ARMAX [25] | Price/EPEX | Spain, Germany | Optimization of functional parameters for price forecasting | Non linearity |

CNN, LSTM [26] | Price/PJM | US | Two NNs are used for price forecasting | Computationally expensive |

DNN [27] | Price/EPEX | Belgium | Complex patterns are extracted for prediction | Space complexity |

GCA, KPCA, DE-SVM [28] | Price/ISO NE-CA | New England | Dimensionality reduction is removed using hybrid of KPCA and GCA | Over fitting |

SDA [29] | Price/MISO | Arkansas, Texas and Indiana | Variant of autoencoder used | Computationally expensive |

ARIMA, TVC-ABC, NLS-SVM [30] | Price/PJM, NYISO, AEMO | Australia, US | Parameter tuning of SVM done using TV-ABC | Computationally expensive |

ANN with meta heuristics optimization methods [31] | Load and price/Commercial load of building in China, Taiwan regional electricity load | Taiwan | Various paramater calculations done for accuracy | Accuracy of models depend on nature of dataset |

OS-ELM with kernel [32] | Load and price/Sylva bench mark | US | Comparison of different algorithms done | Restrict to the computation of streamed data |

ELM in multi class scenario [33] | Load and price/University of California Irvine | Canada | Robust classification | Computational cost overhead |

Enhanced Logistic Regression | Load and Price/UMass Electric Dataset | USA | ELR beats conventional techniques | Large computational time |

RELM enhanced using GWO | Load and Price/UCI Dataset | USA | Optimized weights and biases leads to better prediction | Large computational time is required for weight optimization |

Original Features |
---|

Air Conditioner (AC), Furnace, Cellar lights, Washer, First floor lights, Utility room + Basement, Garage outlets, Master bed + Kids bed, Dryer, Panels, Home office, Dining room, Microwave, Fridge |

Features | Load Values | Price Values |
---|---|---|

AC | 0.6653 | 0.6633 |

Furnace | 0.0103 | 0.0101 |

Cellar lights | 0.0018 | 0.0011 |

Washer | 0.0029 | 0.0029 |

First floor | 0.0032 | 0.0026 |

Utility + Basement | 0.0615 | 0.0670 |

Garage | 0.0036 | 0.0070 |

M. bed + K. bed | 0.0080 | 0.0059 |

Dryer | 0.1890 | 0.1927 |

Panels | 0.0033 | 0.0030 |

Home office | 0.0826 | 0.0083 |

Dining room | 0.0079 | 0.0084 |

Microwave | 0.0296 | 0.0262 |

Type | Number of Features |
---|---|

Original | 16 |

Selected | 8 |

Rejected | 8 |

Parameters | Values |
---|---|

Threshold | 10 |

Selected features | 5 |

Nearest Neighbors | 3 |

Transfer Function | Forecasting Approach | Training | Testing |
---|---|---|---|

ELM | 0.0532 | 0.0535 | |

Hard Limit | RELM | 0.0412 | 0.0423 |

ERELM | 0.0332 | 0.0345 | |

ELM | 0.0513 | 0.0525 | |

Sin | RELM | 0.0352 | 0.362 |

ERELM | 0.0321 | 0.0523 | |

ELM | 0.0634 | 0.0673 | |

Tanh | RELM | 0.0453 | 0.0463 |

ERELM | 0.0341 | 0.0321 | |

ELM | 0.0423 | 0.473 | |

Sigmoid | RELM | 0.0341 | 0.0381 |

ERELM | 0.0214 | 0.0235 |

**Table 10.**Obtained RMSE for half-yearly testing data using ELM, RELM and ERELM by Monte Carlo and K-Fold cross validation.

Datasets | ERELM | RELM | ELM | RNN | LR | |||||
---|---|---|---|---|---|---|---|---|---|---|

Monte Carlo | K-Fold | Monte Carlo | K-Fold | Monte Carlo | K-Fold | Monte Carlo | K-Fold | Monte Carlo | K-Fold | |

MT166 | 0.0235 | 0.0265 | 0.0734 | 0.0788 | 0.0824 | 0.0883 | 0.08234 | 0.0852 | 0.0853 | 0.0873 |

MT168 | 0.0134 | 0.0162 | 0.0421 | 0.0462 | 0.0524 | 0.0423 | 0.0854 | 0.0862 | 0.0756 | 0.0763 |

MT169 | 0.0153 | 0.02352 | 0.0531 | 0.0353 | 0.0382 | 0.0463 | 0.0853 | 0.0873 | 0.0735 | 0.0762 |

MT171 | 0.0354 | 0.0423 | 0.0524 | 0.0552 | 0.0634 | 0.0643 | 0.0854 | 0.0852 | 0.072 | 0.0712 |

MT182 | 0.0242 | 0.0353 | 0.0252 | 0.0352 | 0.0835 | 0.0952 | 0.0753 | 0.0776 | 0.0934 | 0.0952 |

MT235 | 0.0153 | 0.0142 | 0.0344 | 0.0397 | 0.0634 | 0.0643 | 0.0865 | 0.934 | 0.981 | 0.0991 |

MT237 | 0.0243 | 0.0297 | 0.0534 | 0.0535 | 0.0752 | 0.0795 | 0.0756 | 0.0762 | 0.0795 | 0.08255 |

MT249 | 0.0143 | 0.0163 | 0.0524 | 0.0532 | 0.0624 | 0.0693 | 0.0862 | 0.0891 | 0.0753 | 0.0778 |

MT250 | 0.0342 | 0.0452 | 0.0535 | 0.0562 | 0.0853 | 0.0873 | 0.0764 | 0.0784 | 0.0874 | 0.0894 |

MT257 | 0.0242 | 0.0215 | 0.0413 | 0.0413 | 0.0642 | 0.0683 | 0.0753 | 0.0794 | 0.0893 | 0.0934 |

UMass Electric | 0.0398 | 0.0315 | 0.0534 | 0.0563 | 0.0681 | 0.0685 | 0.0712 | 0.0891 | 0.0888 | 0.0913 |

**Table 11.**Obtained RMSE for yearly testing data using ELM, RELM and ERELM by Monte Carlo and K-Fold cross validation.

Datasets | ERELM | RELM | ELM | RNN | LR | |||||
---|---|---|---|---|---|---|---|---|---|---|

Monte Carlo | K-Fold | Monte Carlo | K-Fold | Monte Carlo | K-Fold | Monte Carlo | K-Fold | Monte Carlo | K-Fold | |

MT166 | 0.0224 | 0.0242 | 0.0651 | 0.0665 | 0.0756 | 0.0801 | 0.08732 | 0.0792 | 0.0862 | 0.0851 |

MT168 | 0.0124 | 0.0151 | 0.0634 | 0.0732 | 0.0521 | 0.0410 | 0.0831 | 0.0731 | 0.0701 | 0.0678 |

MT169 | 0.0144 | 0.0224 | 0.0501 | 0.0553 | 0.0424 | 0.0431 | 0.0812 | 0.0912 | 0.0741 | 0.0872 |

MT171 | 0.0142 | 0.0401 | 0.0421 | 0.0538 | 0.0512 | 0.0682 | 0.0781 | 0.0792 | 0.0712 | 0.0882 |

MT182 | 0.0182 | 0.0200 | 0.0242 | 0.0250 | 0.0743 | 0.0791 | 0.0824 | 0.0701 | 0.0892 | 0.0822 |

MT235 | 0.0142 | 0.0152 | 0.0301 | 0.0362 | 0.0582 | 0.0602 | 0.0852 | 0.0892 | 0.0889 | 0.0986 |

MT237 | 0.0224 | 0.0267 | 0.0513 | 0.0521 | 0.0623 | 0.0632 | 0.0701 | 0.0789 | 0.0862 | 0.0813 |

MT249 | 0.0132 | 0.0157 | 0.0421 | 0.0613 | 0.0523 | 0.0623 | 0.0782 | 0.0802 | 0.0671 | 0.0742 |

MT250 | 0.0242 | 0.0273 | 0.0412 | 0.0501 | 0.0602 | 0.0692 | 0.0682 | 0.0772 | 0.0785 | 0.0864 |

MT257 | 0.0324 | 0.0472 | 0.0401 | 0.0513 | 0.0602 | 0.0744 | 0.0623 | 0.0702 | 0.0876 | 0.0882 |

UMass Electric | 0.0332 | 0.0412 | 0.0542 | 0.0552 | 0.0582 | 0.0603 | 0.0701 | 0.0771 | 0.0821 | 0.0891 |

Forecasting Technique | Training Time (s) | Testing Time (s) |
---|---|---|

ERELM | 0.653 | 0.0346 |

RELM | 0.0043 | 0.0012 |

ELM | 0.00124 | 0.001076 |

Metrics | Half-Yearly Data | Yearly Data | ||||
---|---|---|---|---|---|---|

CNN | LR | ELR | CNN | LR | ELR | |

MSE (abs. val) | 8.84 | 5.84 | 4.77 | 10.2 | 8.97 | 6.8 |

MAE (abs. val) | 9.24 | 5.25 | 4.34 | 8.75 | 6.25 | 4.24 |

RMSE (abs. val) | 10.62 | 7.64 | 6.18 | 10.4 | 6.6 | 5.2 |

MAPE (%) | 25.44 | 22.45 | 18.48 | 36.3 | 33.3 | 30.5 |

Accuracy (%) | 89.38 | 92.35 | 93.82 | 89.6 | 93.4 | 94.8 |

Metrics | Half-Yearly Data | Yearly Data | ||||
---|---|---|---|---|---|---|

CNN | LR | ELR | CNN | LR | ELR | |

MSE (abs. val) | 20.2 | 17.97 | 12.97 | 18.9 | 16.5 | 11.3 |

MAE (abs. val) | 8.82 | 6.87 | 5.28 | 8.75 | 6.25 | 5.19 |

RMSE (abs. val) | 16.25 | 13.12 | 10.18 | 15.76 | 12.98 | 9.64 |

MAPE (%) | 25.65 | 22.19 | 17.41 | 33.2 | 25.9 | 22.8 |

Accuracy (%) | 83.75 | 86.88 | 89.81 | 84.24 | 87.02 | 91.36 |

Metrics | Half-Yearly Data | Yearly Data | ||||
---|---|---|---|---|---|---|

CNN | LR | ELR | CNN | LR | ELR | |

MSE (abs. val) | 25.82 | 21.82 | 17.37 | 24.02 | 20.56 | 14.25 |

MAE (abs. val) | 10.55 | 8.23 | 6.79 | 10.35 | 8.15 | 5.33 |

RMSE (abs. val) | 17.85 | 14.77 | 11.79 | 12.55 | 9.98 | 6.52 |

MAPE (%) | 29.13 | 27.13 | 23.39 | 25.45 | 21.2 | 20.6 |

Accuracy (%) | 82.15 | 85.72 | 88.21 | 87.45 | 90.02 | 93.48 |

Metrics | Half-Yearly Data | Yearly Data | ||||
---|---|---|---|---|---|---|

CNN | LR | ELR | CNN | LR | ELR | |

MSE (abs. val) | 15.08 | 14.39 | 10.09 | 12.58 | 10.85 | 8.6 |

MAE (abs. val) | 8.25 | 7.65 | 6.01 | 7.85 | 7.05 | 5.88 |

RMSE (abs. val) | 16.63 | 14.99 | 12.98 | 15.05 | 11.52 | 9.85 |

MAPE (%) | 19.02 | 18.59 | 17.11 | 20.05 | 18.85 | 15.55 |

Accuracy (%) | 83.37 | 85.01 | 87.02 | 84.95 | 88.48 | 90.15 |

Metrics | Half-Yearly Data | Yearly Data | ||||
---|---|---|---|---|---|---|

CNN | LR | ELR | CNN | LR | ELR | |

MSE (abs. val) | 14.05 | 12.80 | 11.22 | 15.02 | 13.45 | 11.25 |

MAE (abs. val) | 7.55 | 6.04 | 5.03 | 8.02 | 7.05 | 5.25 |

RMSE (abs. val) | 13.05 | 11.30 | 9.47 | 12.55 | 10.45 | 8.64 |

MAPE (%) | 14.25 | 13.71 | 13.03 | 16.45 | 15.75 | 15.25 |

Accuracy (%) | 86.95 | 88.70 | 90.53 | 87.45 | 89.55 | 91.36 |

Metrics | Half-Yearly Data | Yearly Data | ||||
---|---|---|---|---|---|---|

CNN | LR | ELR | CNN | LR | ELR | |

MSE (abs. val) | 19.45 | 18.91 | 16.47 | 20.05 | 18.54 | 13.35 |

MAE (abs. val) | 8.95 | 7.70 | 6.44 | 9.35 | 8.15 | 6.42 |

RMSE (abs. val) | 14.78 | 13.75 | 11.48 | 12.44 | 11.02 | 9.45 |

MAPE (%) | 21.44 | 20.54 | 18.89 | 23.36 | 22.55 | 19.45 |

Accuracy (%) | 85.22 | 86.25 | 88.52 | 87.56 | 88.98 | 90.55 |

Metrics | Half-Yearly Data | Yearly Data | ||||
---|---|---|---|---|---|---|

CNN | LR | ELR | CNN | LR | ELR | |

MSE (abs. val) | 15.05 | 12.47 | 10.56 | 18.20 | 14.3 | 10.4 |

MAE (abs. val) | 12.45 | 10.34 | 8.56 | 21.47 | 18.37 | 16.61 |

RMSE (abs. val) | 18.52 | 15.54 | 13.45 | 16.22 | 13.78 | 10.16 |

MAPE (%) | 28.24 | 25.34 | 20.45 | 27.05 | 23.25 | 20.05 |

Accuracy (%) | 81.48 | 84.46 | 86.55 | 83.78 | 86.22 | 89.84 |

Metrics | Half-Yearly Data | Yearly Data | ||||
---|---|---|---|---|---|---|

CNN | LR | ELR | CNN | LR | ELR | |

MSE (abs. val) | 25.20 | 19.66 | 15.77 | 13.25 | 8.34 | 7.2 |

MAE (abs. val) | 11.35 | 10.01 | 8.24 | 13.98 | 12.47 | 11.39 |

RMSE (abs. val) | 22.45 | 19.25 | 16.45 | 20.25 | 17.80 | 13.11 |

MAPE (%) | 28.56 | 25.45 | 19.63 | 30.50 | 25.45 | 18.52 |

Accuracy (%) | 77.55 | 80.75 | 83.55 | 79.75 | 82.20 | 86.89 |

Metrics | Half-Yearly Data | Yearly Data | ||||
---|---|---|---|---|---|---|

CNN | LR | ELR | CNN | LR | ELR | |

MSE (abs. val) | 28.35 | 25.55 | 21.68 | 15.50 | 13.8 | 5.47 |

MAE (abs. val) | 15.35 | 10.34 | 8.95 | 23.46 | 19.3 | 17.7 |

RMSE (abs. val) | 23.97 | 20.87 | 17.69 | 20.02 | 17.17 | 14.49 |

MAPE (%) | 31.23 | 29.43 | 25.67 | 27.45 | 25.35 | 20.02 |

Accuracy (%) | 76.03 | 79.13 | 82.31 | 79.98 | 82.23 | 85.51 |

Datasets | RMSE | MSE | MAE |
---|---|---|---|

MT166 | 0.0235 | 0.00055 | 0.0243 |

MT168 | 0.0134 | 0.00017 | 0.0135 |

MT169 | 0.0153 | 0.00023 | 0.0174 |

MT171 | 0.0354 | 0.00125 | 0.0352 |

MT182 | 0.0242 | 0.00058 | 0.0252 |

MT235 | 0.0153 | 0.00023 | 0.0253 |

MT237 | 0.0243 | 0.00059 | 0.0254 |

MT249 | 0.0143 | 0.00020 | 0.0153 |

MT250 | 0.0342 | 0.001169 | 0.0342 |

MT257 | 0.0242 | 0.00058 | 0.0253 |

UMass Electric | 0.0256 | 0.00071 | 0.0623 |

Arithmetic Mean | 0.0227 | 0.00055 | 0.024218 |

Standard Deviation | 0.00600 | 0.000350 | 0.006515 |

Datasets | RMSE | MSE | MAE |
---|---|---|---|

MT166 | 0.0224 | 0.00041 | 0.0215 |

MT168 | 0.0124 | 0.00016 | 0.0142 |

MT169 | 0.0144 | 0.00015 | 0.0162 |

MT171 | 0.0142 | 0.00124 | 0.0221 |

MT182 | 0.0200 | 0.00042 | 0.0224 |

MT235 | 0.0142 | 0.00047 | 0.0201 |

MT237 | 0.0224 | 0.00015 | 0.0241 |

MT249 | 0.0132 | 0.00012 | 0.0142 |

MT250 | 0.0242 | 0.00102 | 0.0163 |

MT257 | 0.0324 | 0.00045 | 0.0177 |

UMass Electric | 0.0332 | 0.00061 | 0.0546 |

Arithmetic Mean | 0.02027 | 0.00047 | 0.02212 |

Standard Deviation | 0.00712 | 0.00034 | 0.01077 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Naz, A.; Javed, M.U.; Javaid, N.; Saba, T.; Alhussein, M.; Aurangzeb, K. Short-Term Electric Load and Price Forecasting Using Enhanced Extreme Learning Machine Optimization in Smart Grids. *Energies* **2019**, *12*, 866.
https://doi.org/10.3390/en12050866

**AMA Style**

Naz A, Javed MU, Javaid N, Saba T, Alhussein M, Aurangzeb K. Short-Term Electric Load and Price Forecasting Using Enhanced Extreme Learning Machine Optimization in Smart Grids. *Energies*. 2019; 12(5):866.
https://doi.org/10.3390/en12050866

**Chicago/Turabian Style**

Naz, Aqdas, Muhammad Umar Javed, Nadeem Javaid, Tanzila Saba, Musaed Alhussein, and Khursheed Aurangzeb. 2019. "Short-Term Electric Load and Price Forecasting Using Enhanced Extreme Learning Machine Optimization in Smart Grids" *Energies* 12, no. 5: 866.
https://doi.org/10.3390/en12050866